Datasheet
Data Sheet ADP1822
Rev. D | Page 17 of 24
then use both the ESR zero and feed-forward zeros to stabilize
the regulator (see the Compensation Using Both the ESR and
Feed-Forward Zeros section).
In all three cases, it is sometimes beneficial, although not required,
to add an additional compensation capacitor, C
C2
, from COMP
to FB to reduce high frequency noise. This capacitor forms an
extra pole in the loop response. Choose this capacitor such that
the pole occurs at approximately 1/2 of the switching frequency, or
( )( )
COMPCCOMP
SW
PC
RCCπ
f
f
2
2
//2
1
2
==
(24)
Assuming C
COMP
>> C
C2
, then solving for C
C2
,
( )( )
COMPSW
C
Rf
C
π2
2
2
=
(25)
Compensation Using the ESR Zero
V
OUT
TO
PWM
COMP
FB
0.6V
R
COMP
C
COMP
C
C2
R
TOP
R
BOT
INTERNAL ERROR AMPLIFIER
05311-003
Figure 19. Compensation Using the ESR Zero
If the output capacitor ESR zero is sufficiently low (less than or
equal to 1/2 of the crossover frequency), use the ESR to stabilize
the regulator. In this case, use the circuit shown in Figure 19.
Choose the compensation resistor to set the desired crossover
frequency, typically 1/10 of the switching frequency or
( )
( )
( )
( )
( )
2
LC
IN
CO
ESRZ
RAMP
TOP
COMP
fV
ffVR
R =
(26)
where:
R
COMP
is the compensation resistor.
V
RAMP
is the internal ramp peak voltage, 1.25 V.
f
ESRZ
and f
CO
are the ESR zero and crossover frequencies.
V
IN
is the dc input voltage.
f
LC
is the characteristic frequency of the output LC filter, or
LC
f
LC
π2
1
=
(27)
using known constants
( )( )
( )
( )
( )
IN
SW
ESRZTOP
COMP
V
CLffR
R
9.4
≅
(28)
Choose the compensation capacitor to set the compensation
zero, f
ZC
, to the lesser of 1/4 of the crossover frequency or 1/2 of
the LC resonant frequency, or
( )( )
COMPCOMP
SWCO
ZC
RC
ff
f
π2
1
404
===
(29)
or
( )( )
COMPCOMP
LC
ZC
RC
f
f
π2
1
2
==
(30)
Solving for C
COMP
,
( )( )
COMPCO
COMP
Rf
C
π2
4
=
(31)
In terms of the switching frequency and combining the constants,
( )( )
COMPSW
COMP
Rf
C
37.6
≅
(32)
or
( )( )
COMPLC
COMP
Rf
C
π2
2
=
(33)
or whichever is greater.
Compensation Using Feed-Forward
V
OUT
TO
PWM
COMP
FB
0.6V
R
COMP
C
COMP
R
TOP
R
BOT
R
FF
C
FF
INTERNAL ERROR AMPLIFIER
05311-004
C
C2
Figure 20. Compensation Using Feed-Forward
If the ESR zero is at too high a frequency to be useful in
stabilizing the regulator, add a series RC network, as shown in
Figure 20, in parallel with the top side voltage divider resistor,
R
TOP
. This adds an additional zero and pole pair that is used to
increase the phase at crossover, thus improving stability.
Choose the feed-forward zero frequency for 1/7 of the crossover
frequency, and the feed-forward pole at 7× the crossover
frequency. This sets the ratio of pole-to-zero frequency of
approximately 50:1 for optimum stability.
Choose the compensation resistor, R
COMP
, to set the crossover
frequency by
( )
( )( )( )
( )
2
LC
IN
CO
ZFF
RAMP
TOP
COMP
fV
ffVR
R =
(34)
where f
ZFF
is the feed-forward zero frequency and is 1/7 of the
crossover frequency. Simplify the following equation:
( )
( )
( )
( )
IN
SW
TOP
COMP
V
CLfR
R
2
0705.0≅
(35)